We characterize the role of the impulse transmitted (time integral over a half-period) by resonant secondary excitations at controlling (suppressing and enhancing) escape from a potential well, which is induced by periodic primary excitations. By using the universal model of a dissipative Helmholtz oscillator, we demonstrate numerically that optimum control of escape occurs when the impulse transmitted by the chaos-controlling excitations is maximum while keeping their amplitude and period fixed. These findings are in complete agreement with analytical predictions from two independent methods: Melnikov analysis and energy-based analysis. Additional numerical results corresponding to other alternative escape-controlling excitations demonstrate the generality of the essential role of the excitation's impulse.

• Received 16 February 2012

DOI:https://doi.org/10.1103/PhysRevE.85.066207